So, according to the Emacs manual, you can create inactive timestamps of the form [1970-01-01 Thu] by hitting C-c !.
However, doing so will result in my minibuffer displaying C-c !- waiting for further input. Hitting space or return doesn't work and just results in an error saying C-c !-RET isn't a valid command.
What exactly happened here? Is the command simply not defined by default? I'm fairly certain I don't have anything defined that globally overrides this, but I could be wrong.
If you type C-c ! <f1> you'll see a list of all keybindings that start with C-c !. Does that help?
I don't think there's a timestamp function bound to C-c ! by default, but there are plenty of results if you Google "Emacs timestamp".